We investigate equilibrium statistical properties of a disordered urn model. New types of urn models are proposed, in which quenched disorder parameters play an important role in generating power-law behavior. We evaluate the occupation probability P (k) with which an urn has k balls by using the concept of statistical physics of disordered systems. In our new disordered urn model, we find that...

The generalized Pólya urn has been extensively studied and is widely applied in many disciplines. An important application of urn models is in the development of randomized treatment allocation schemes in clinical studies. The randomly reinforced urn was recently proposed, but, although the model has some intuitively desirable properties, it lacks theoretical justification. In this paper we obt...

Recent studies have indicated that the coarse grained dynamics of a large class of traffic models and driven-diffusive systems may be described by urn models. We consider a class of one-dimensional urn models whereby particles hop from an urn to its nearest neighbor by a rate which decays with the occupation number k of the departure site as (1 + b/k). In addition a diffusion process takes plac...

In this paper, using generalized {polya} urn models we find the expected value of the size of a branch in recursive $k$-ary trees. We also find the expectation of the number of nodes of a given outdegree in a branch of such trees.